In this paper we consider a general class $\mathcal E $ of self-similar sets with complete
overlaps. Given a self-similar iterated function system $\Phi=(E,\{f_i\} _ {i= 1}^ m)\in\mathcal …

Abstract Let A, B⊂ R. Define A⋅ B={x⋅ y: x∈ A, y∈ B}. In this paper, we consider the
following class of self-similar sets with overlaps. Let K be the attractor of the IFS {f 1 (x)= λ x, f …

In this paper we consider a general class E of self-similar sets with complete overlaps. Given
a self-similar iterated function system Φ=(E,{fi} i= 1 m)∈ E on the real line, for each point x∈ …

Suppose $ n\geq 2$ and $\mathcal {A} _ {i}\subset\{0, 1,\cdots,(n-1)\} $ for $ i= 1,\cdots, l, $
let $ K_ {i}=\bigcup\nolimits_ {a\in\mathcal {A} _ {i}} n^{-1}(K_ {i}+ a) $ be self-similar sets …

Unique expansions in non-integer bases have been investigated in many papers during the
last thirty years. They are often conveniently generated by labeled directed graphs. We give …

Let M be a positive integer and q∈(1, M+ 1]. A q-expansion of a real number x is a
sequence (ci)= c 1 c 2⋯ with ci∈{0, 1,…, M} such that x=∑ i= 1∞ ciq− i. Let U qj denote the …

Estimating the Hausdorff dimensions of univoque sets for self-similar sets - ScienceDirect
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In this paper, we consider a class of self-similar sets, denoted by A, and investigate the set of
points in the self-similar sets having unique codings. We call such set the univoque set and …

Mattila and Saaranen gave an elegant decomposition of the Ahlfors-David regular set [15,
Lemma 2.2]. Motivated by their work, in this paper, we define the configuration set and …

Unique expansions in non-integer bases $ q $ have been investigated in many papers
during the last thirty years. They are often conveniently generated by labeled directed …